When the Sun is directly overhead, a hawk
dives toward the ground at a speed of
6.09 m/s.
If the direction of his motion is at an angle
of 78.6
â—¦ below the horizontal, calculate the
speed of his shadow along the ground.
Answer in units of m/s
To calculate the speed of the hawk's shadow along the ground, we can use trigonometry. The speed of the shadow is the horizontal component of the hawk's velocity. We need to find the horizontal component of the hawk's velocity.
Given:
Speed of the hawk = 6.09 m/s
Angle below the horizontal = 78.6 degrees
To find the horizontal component, we can use the cosine function:
Horizontal component = Speed of the hawk * cos(Angle below the horizontal)
Plugging in the values:
Horizontal component = 6.09 m/s * cos(78.6 degrees)
Now we need to calculate the cosine of 78.6 degrees. Using a scientific calculator or online calculator:
cos(78.6 degrees) = 0.2128
To find the horizontal component:
Horizontal component = 6.09 m/s * 0.2128
Horizontal component = 1.299 m/s
Therefore, the speed of the hawk's shadow along the ground is approximately 1.299 m/s.
I am going to assume a flat and earth and the sun at infinity :)
In that case the tip of the hawk's shadow is directly under the hawk and moves at the hawk's horizontal speed.
u = 6.09 cos 78.6